County employees will get a raise and taxpayers will pay a bit more to fund county services, according to the package of budget amendments the Fairfax County Board of Supervisors approved on Tuesday.

That package did not include any additional money for schools. The county is planning to fund $1.68 billion in school operations costs, a 4.5 percent increase over the current year’s budget; school officials had asked for as much as an 8 percent increase.

The board formally will adopt the $6.3 billion budget and set the county’s real estate tax rate for fiscal 2013 on May 1.

Supervisors plan to increase the county’s real estate tax rate by 0.5 cents ( to $1.075 per $100 of assessed value) and increase the stormwater tax by 0.5 cents, to 2 cents per $100 of assessed value. The stormwater service fee is billed as part of residents’ real estate taxes.

The combined rate increases represent an average $80 increase for homeowners.

Supervisor Jeff McKay (D-Lee) said that, given the increase in his assessed home value, he actually would be seeing a more than $700 increase in his own tax bill.

“It is worth it to me to provide the services that we heard from the community that they need,” he said.

Supervisor Pat Herrity (R-Springfield) was one of two supervisors to vote against the budget package because of tax increases. He said he supports increasing employee salaries but opposes other expenditures, such as funding for affordable housing programs.

“We need to be preparing for the future, and this budget fails to do that,” Herrity said.

Supervisor John Cook (R-Braddock) also voted against the budget amendments. He said the increased spending on county programs is shortchanging investments in transportation and other infrastructure.

Board members agreed to increase the stormwater service fee less to offset the half-cent increase in the real estate tax rate. This move allowed the board to invest more funding in employee salaries than Griffin originally had proposed.

Non-public safety employees will receive a 2.18 percent cost-of-living increase in July, and will be eligible for a performance-based pay increase of as much as 2.5 percent in January. Public safety employees also will receive a cost-of-living increase and be eligible to receive their scheduled longevity-based pay increases on their anniversary dates.

The total cost for these pay increases is about $39 million, and an additional $38 million is included in the budget to cover increases in retirement, health insurance and other employee benefits.

“I think that our employees have done a tremendous amount over the years without increases in compensation,” said Supervisor Michael Frey (R-Sully), adding compensation was his biggest budget priority. “We could not wait another year.”

In addition to investing more in employee compensation, the board also voted to put $5.6 million more into human services programs and an additional $1.3 million for the county’s affordable housing plan.

Some library hours that were cut in recent years will be restored, specialized public safety positions such as the two-person marine patrol — which supervisors jokingly call “Fairfax County’s navy” — were spared again, and there was even $100,000 to support local arts organizations.

“Hopefully we are beginning to see the dawn of a new day,” said board Chairwoman Sharon Bulova (D-At large), expressing optimism that the tough budget years due to the nationwide recession are behind the county.